Nope; I have to do the same thing on our 1 Star. Fortunately taking off the lid is pretty easy. When you remove the two hinge screws (one on either side) there are some thick in-line shims/washers you have to be sure to catch, and be sure to remember to put them back on when replacing the lid.
Once the lid is off it's a simple matter of turning it over and scraping/scrubbing the flaky black stuff off, then spraying it down with a hose.
Of course, I'm sharing this not having a 2 Star, but as far as I know taking the lid off is the same as the 1 Star. If I am wrong, someone will chime in.